The second group of essays from the 2022 Teddy Rocks Maths Competition come from entrants with surnames beginning with the letters C-D. The showcase will take place throughout May and June with the winners being announced at the end.

The competition was organised with St Edmund Hall at the University of Oxford and offers a cash prize plus publication on the university website. It will be running again in early 2023 so be sure to follow Tom (Instagram, Twitter, Facebook, YouTube) to make sure you don’t miss the announcement!

All essays can be read in full (as submitted) by clicking on the title below. If you enjoy any of them please let the author know by leaving a comment – enjoy!

John explores the infinite and demonstrates how the natural numbers and even numbers are in fact the same size.

Dominic catalogues the research into maths anxiety and whether creative teaching could be successful in tackling the issue.

Hyunseo introduces Reuleaux Polygons and their relationship to Barbier’s Theorem and the Isoperimetric Inequality.

Aditi explains how neural networks work through the gradient descent method and minimisation of the loss function.

Yinan identifies three common misunderstandings of the Monty Hall Problem, and shows that the probability of success will always increase when switching in the general case of n doors.

Madhav takes us on a tour of large numbers from Graham’s Number and Tree(3), to the Busy Beaver function and Rayo’s Number.

Tsz Yau Alisa explains the link between musical notes and the fractional scales first identified by Pythagoras.

Tanmay documents the history of Elliptic Curves from their discovery in Ancient Greece, to their modern-day use in Cryptocurrencies such as Bitcoin.

Aditya discusses the Collatz Conjecture – outlining what it is, and the progress mathematicians have made in the search for a proof.

Alex highlights the connections between Mathematics and Philosophy with examples from the Ancient Civilisations, and more recent struggles with the concepts of infinity and set theory.

Cattien explains Godel Numbers and how they were used by Godel to create a self-referential mathematical statement that could never be proven nor disproven.